Diffusion entropy approach to complexity for a Hodgkin–Huxley neuron

Yang, Huijie; Zhao, Fangcui; Zhang, Wei; Li, Zhongnan

doi:10.1016/j.physa.2004.08.017

Cited by 16 publications

(12 citation statements)

References 14 publications

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“…It is the first tool yielding correct scalings in both the Gaussian and the Lévy statistics. For this reason, it is used to detect scale-invariance in diverse research fields [43] , such as solar activities [44] – [48] , spectra of complex networks [49] , physiological signals [50] – [54] , DNA sequences [55] , [56] , geographical phenomena [57] – [59] , and finance [51] , [60] .…”

Section: Methodsmentioning

confidence: 99%

Evaluation of Scaling Invariance Embedded in Short Time Series

et al. 2014

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Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length . Calculations with specified Hurst exponent values of show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias () and sharp confidential interval (standard deviation ). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

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Section: Methodsmentioning

confidence: 99%

Evaluation of Scaling Invariance Embedded in Short Time Series

et al. 2014

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“…where A is a constant depends on the PDF. Detailed works show that DE is a reliable method to search the correct value of δ, regardless the form of the PDF [26,27,28,29]. The complexity in the PDF can be catalogued into two levels [30], the primary one due to the extension of the probability to all the possible displacements m, and the secondary one due to the internal structures.…”

Section: Diffusion Entropy Analysismentioning

confidence: 99%

Complexities of human promoter sequences

Zhao¹,

Yang²,

Wang³

2007

Journal of Theoretical Biology

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By means of the diffusion entropy approach, we detect the scale-invariance characteristics embedded in the 4737 human promoter sequences. The exponent for the scale-invariance is in a wide range of [0.3,0.9], which centered at delta(c)=0.66. The distribution of the exponent can be separated into left and right branches with respect to the maximum. The left and right branches are asymmetric and can be fitted exactly with Gaussian form with different widths, respectively.

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“…The DEA method has been used to analysis many time series in different research fields, such as the solar induced atmosphere temperature series [22], the intermittency time series in fluid turbulence [23], the spectra of complex networks [24], the output spike trains of neurons [25], the index of financial market [26], and so on.…”

Section: Diffusion Entropy Technique Based On Fourier Analysismentioning

confidence: 99%

Diffusion entropy analysis on the stride interval fluctuation of human gait

Cai

Zhou

Yang

et al. 2007

Physica A: Statistical Mechanics and its Applications

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In this paper, the diffusion entropy technique is applied to investigate the scaling behavior of stride interval fluctuations of human gait. The scaling behavior of the stride interval of human walking at normal, slow and fast rate are similar; with the scale-invariance exponents in the interval [0.663, 0.955], of which the mean value is 0.821 ± 0.011. Dynamical analysis of these stride interval fluctuations reveals a self-similar pattern: Fluctuation at one time scale are statistically similar to those at multiple other time scales, at least over hundreds of steps, while the healthy subjects walk at their normal rate. The long-range correlations are observed during the spontaneous walking after the removal of the trend in the time series with Fourier filter. These findings uncover that the fractal dynamics of stride interval of human gait are normally intrinsic to the locomotor systems.

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Diffusion entropy approach to complexity for a Hodgkin–Huxley neuron

Abstract: By means of the concept DE we analyze the responses of a HH neuron to two types of spike-train inputs. Two characteristic quantities can be extracted, which can reflect partially the dynamical process of a HH neuron.

Cited by 16 publications

References 14 publications

Evaluation of Scaling Invariance Embedded in Short Time Series

Evaluation of Scaling Invariance Embedded in Short Time Series

Complexities of human promoter sequences

Diffusion entropy analysis on the stride interval fluctuation of human gait

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